Math 2250
Week 3 Quiz
Name, UID, and section TA:
Write your answer in the space provided. Show work for full credit. There is
a third problem on the back of this page.
1. (3 points) Consider the following differential equation for x(t), which could be modeling
a logistic differential equation with harvesting
x0 (t) = −x2 + 3x − 2.
Find the equilibrium solutions. Then draw the phase diagram and indicate the stability
for each equilibrium solution.
2. (3 points) Compute the partial fractions decomposition for
1
.
(x − 1)(x − 2)
3. (4 points) Use your work from (2) to solve the initial value problem
x0 (t) = −x2 + 3x − 2
x(0) = 3
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